Eilenberg-MacLane Spaces, Cohomology, and Principal Fibrations
Postnikov Towers and Rational Homotopy Theory
deRham's theorem for simplicial complexes
Differential Graded Algebras
Homotopy Theory of DGAs
DGAs and Rational Homotopy Theory
The Fundamental Group
Examples and Computations
Functorality
The Hirsch Lemma
Quillen's work on Rational Homotopy Theory
A1-structures and C1-structures
Exercises.
Summary:
Rational homotopy theory is today one of the major trends in algebraic topology. Despite the great progress made in only a few years, a textbook properly devoted to this subject still was lacking until now The appearance of the text in book form is highly welcome, since it will satisfy the need of many interested people. Moreover, it contains an approach and point of view that do not appear explicitly in the current literature. Zentralblatt MATH (Review of First Edition) The monograph is intended as an introduction to the theory of minimal models. Anyone who wishes to learn about the theory will find this book a very helpful and enlightening one. There are plenty of examples, illustrations, diagrams and exercises. The material is developed with patience and clarity. Efforts are made to avoid generalities and technicalities that may distract the reader or obscure the main theme. The theory and its power are elegantly presented. This is an excellent monograph. Bulletin of the American Mathematical Society (Review of First Edition) This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Thams theorem on simplical complexes. In addition, Sullivans results on computing the rational homotopy type from forms is presented.